Suppose there are two types of food: Slow and Fast. Slow food is food that takes a lot of time and energy to prepare, and is possibly more "authentic." Consider it a high-end luxury good. All other food we'll call Fast. It's a staple needed to live, is quick to acquire and cheap. The slow food costs $20 per unit, while the fast food costs $5 per unit. The price elasticity of demand for slow food is -2.8. The price elasticity of demand for fast food is -.20. The government is considering a tax on food. The tax on slow food is denoted t_s, and the tax on fast food is denoted t_f.

1. Comment on the significance of the different elasticities of demand.
2. What is the equation for the optimal (Ramsey) value of t_s in terms of t_f?
3. In a clearly written paragraph, comment on the relative size of t_scompared to t_f, and why we are seeing this result.
4. Suppose the government has selected tax levels t_s and t_f using the Ramsey rule. Furthermore, at those taxes, the market sells 3 million units of slow food and 300 million units of fast food., the government collects $1 billion in revenue from these taxes. What are the values of t_s and t_f?